臺灣博碩士論文加值系統

本文以數值分析方法探討流過一對並列圓柱之流場，流場藉由 Navier-Stokes 方程及連續方程求解。對不穩定、具黏滯性且不可壓縮流流場，為求解複雜邊界，採用沈浸邊界法，並配合巢狀網格進行數值模擬。解答過程採用分步法，含複雜邊界之障礙物則以內嵌法處理之，網格系統採用正交、結構化，具局部加密效果之巢狀卡式網格系統。因此，本文首先系統化解析此流過一對並排圓流場，圓場選取雷諾數(Re)介於40~100 之間，以及間距比(G)介於0.4~1.4 間之所有流場。含似單一渦漩逸出、雙渦漩逸出、對稱流場、偏斜流場、抖動、翻拍、穩定狀態、具規則震盪之週期性之渦漩逸出、似週期、混亂渦漩逸出流場等多樣化渦漩逸出流場型態，均出現在本論文中。

In this paper, a numerical analysis method to investigate the flow through a pair of parallel cylindrical different spacing than the ilk field, flow field is solved by the Navier-Stokes equation and continuity equation. The nested Cartesian grid method is developed for simulating unsteady. In combination with an effective immersed boundary method and a two-step fractional-step procedure, has been adopted to simulate the flows.Therefore,this article first systematic analytic flow through a pair of side-by-side circular flow field, to smooth things over selected Reynolds number (Re) between 40 and 100, and the spacing ratio (G) all of the flow field in the range of 0.4 to 1.4. Contains semi-single vortex shedding street、twin vortex shedding streets、symmetric、deflected、trembled、flip-flopped、steady state、vortex shedding periodically、vortex shedding quasi、by vortex confusion, vortex escape the flow field, such as diversification of the vortex to escape the flow structure, described the development of high efficiency and high accuracy, nested grids.Tested by the nested grid method to flow through symmetrically placed in the channel, the two circular cylindrical obstacle logistics field, to arrive at the average lift drag coefficient, the change of vortex escape, and thus accurately predict the occurrence of vortex escape critical Reynolds number.

中文摘要 III
ABSTRACT IV
目錄 V
圖目錄 VI
表目錄 IX
符號索引 X
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究目的 3
1.4 本文大綱 4
第二章 理論方法 5
2.1 分步法(Fractional Step Method) 5
2.2 內嵌法(Embedding Method) 8
2.3 巢狀網格加密法 10
2.3.1 對流-擴散步驟 11
2.3.2 計算 和 14
2.3.3 求解壓力項 14
2.3.4 速度的修正 16
第三章 網格與數值方法驗證 18
3.1 內嵌法驗證 - 以Wannier Flow為測試流場 18
3.2 巢狀網格加密法之檢驗 21
3.2.1 強曳穴流 21
3.2.2 渠道內流過單一圓形柱體之流場 26
3.2.3 隨不同參數流過兩個相同直徑圓形體 33
第四章 流過一對不同間距比並列圓柱之渦漩逸出流場 37
4.1 網格系統與計算邊界對流場計算結果之影響 37
4.2 流過一對並列圓柱渦漩逸出流場分析-含等渦度圖，昇阻力之時序圖 41
4.3 流過一對並列圓柱不同間距比之臨界雷諾數 55
第五章 結論 59
參考文獻 60
圖目錄
圖 1 分步法之網格配置圖。 5
圖 2巢狀網格加密法 11
圖 3 WANNIER FLOW之幾何外觀、邊界條件以及計算流線圖 19
圖 4 WANNIER FLOW之數值計算誤差，300×150均勻網格計算結果 20
圖 5 內嵌法採不同網格數計算WANNIER FLOW之數值誤差 21
圖 6 B2G3之計算範圍、邊界條件、模擬渦漩輪廓圖以及網格系統 23
圖 7 方形強曳穴流在RE=1000時速度分量U值沿垂直中心線 (X=0.5) 之分佈圖 24
圖 8 方形強曳穴流在RE=1000時沿垂直中心線U值分佈之局部放大圖 24
圖 9方形強曳穴流在RE=1000時速度分量V值沿水平中心線 (Y=0.5) 之分佈圖 25
圖 10 方形強曳穴流在RE=1000時沿水平中心線V值分佈之局部放大圖 26
圖 11 模擬流體流過單一圓柱對稱置放於水平渠道內的配置圖 27
圖 12 由B2D1到B2D8之加密網格範圍圖 27
圖 13計算B3G3網格系統在RE=500時流過單一圓形柱體之渠道內尾流附近的渦漩輪廓圖 30
圖 14 在RE=500時流過單一圓形柱體之渠道內尾波流附近計算B3G3之數值結 31
圖 15 在RE=500時流過單一圓形柱體之渠道內尾波流附近計算B3G3之數值結果的V值輪廓圖 31
圖 16 在RE=500時流過單一圓形柱體之渠道內尾波流附近計算B3G3之數值結果的P值輪廓圖 32
圖 17 與RE的函數關係圖 33
圖 18模擬流過兩個不同直徑的圓柱之流場配置圖 35
圖 19 流過單一圓柱 計算結果隨雷諾數分佈圖 36
圖 20流過單一圓柱ST計算結果隨雷諾數分佈圖 36
圖 21 單層網格系統不同粗細之臨界雷諾數 38
圖 22 雙層網格系統加密區域示意圖 38
圖 23 單層網格系統與雙層網格加密系統圖 39
圖 24 三層網格系統加密區域示意圖 40
圖 25 單層網格系統、雙層網格與三層網格加密系統圖 40
圖 26 雙層網格系統加密區域示意圖 41
圖 27 流體流過間距0.4之雙圓柱RE=53之等渦度圖 44
圖 28 間距0.4之雙圓柱RE=53之 阻力係數時序圖 44
圖 29 間距0.4之雙圓柱RE=53之 昇力係數時序圖 44
圖 30 流體流過間距0.4之雙圓柱RE=54之等渦度圖 45
圖 31 間距0.4之雙圓柱RE=54之 阻力係數時序圖 45
圖 32 間距0.4之雙圓柱RE=54之 昇力係數時序圖 45
圖 33 流體流過間距0.4之雙圓柱RE=58之等渦度圖 46
圖 34 間距0.4之雙圓柱RE=58之 阻力係數時序圖 46
圖 35 間距0.4之雙圓柱RE=58之 昇力係數時序圖 46
圖 36 流體流過間距0.4之雙圓柱RE=60之等渦度圖 47
圖 37 間距0.4之雙圓柱RE=60之 阻力係數時序圖 47
圖 38 間距0.4之雙圓柱RE=60之 昇力係數時序圖 47
圖 39 流體流過間距0.4之雙圓柱RE=78之等渦度圖 48
圖 40 間距0.4之雙圓柱RE=78之 阻力係數時序圖 48
圖 41 間距0.4之雙圓柱RE=78之 昇力係數時序圖 48
圖 42 流體流過間距0.4之雙圓柱RE=80之等渦度圖 49
圖 43 間距0.4之雙圓柱RE=80之 阻力係數時序圖 49
圖 44 間距0.4之雙圓柱RE=80之 昇力係數時序圖 49
圖 45 流體流過間距1.4之雙圓柱RE=47之等渦度圖 50
圖 46 間距1.4之雙圓柱RE=47之 阻力係數時序圖 50
圖 47 間距1.4之雙圓柱RE=47之 昇力係數時序圖 50
圖 48 流體流過間距1.4之雙圓柱RE=48之等渦度圖 51
圖 49 間距1.4之雙圓柱RE=48之 阻力係數時序圖 51
圖 50 間距1.4之雙圓柱RE=48之 昇力係數時序圖 51
圖 51 流體流過間距1.4之雙圓柱RE=55之等渦度圖 52
圖 52 間距1.4之雙圓柱RE=55之 阻力係數時序圖 52
圖 53 間距1.4之雙圓柱RE=55之 昇力係數時序圖 52
圖 54 流體流過間距1.4之雙圓柱RE=70之等渦度圖 53
圖 55 間距1.4之雙圓柱RE=70之 阻力係數時序圖 53
圖 56 間距1.4之雙圓柱RE=70之 昇力係數時序圖 53
圖 57 流體流過間距1.4之雙圓柱RE=75之等渦度圖 54
圖 58 間距1.4之雙圓柱RE=75之 阻力係數時序圖 54
圖 59 間距1.4之雙圓柱RE=75之 昇力係數時序圖 54
圖 60 流過雙圓柱，間距比G=0.4，發生渦漩溢出流場之臨界雷諾數RECR,V 57
圖 61 流過雙圓柱，間距比G=0.4，發生非對稱間隙射流場之臨界雷諾數RECR,D 57
圖 62 流過雙圓柱，間距比G=1.4，發生渦漩溢出流場之臨界雷諾數RECR,V 57
表目錄
表 1 不同網格系統計算 WANNIER FLOW (RE = 0.01) 所需之CPU時間表 21
表 2 1層網格和2層網格的平均阻力係數及昇力振幅之計算結果 27
表 3 1層網格、2層網格、3層網格的平均阻力係數、昇力振幅、 STROUHAL 數及 CPU 時間之計算結果 29
表 4 G=0.4，流過兩圓柱流場計算結果 55
表 5 G=1.4，流過兩圓柱流場計算結果 56

1.Peng, Y.F., Shiau, Y.H., Hwang, Robert R., and Hu, C.K., “Multistability and symmetry breaking in the 2-D flow around a square cylinder,” Physical Review E, Vol. 60, pp. 6188-6191 (1999).
2.Peskin, C. S., “Flow patterns around heart valves: a digital computer method for solving the equations of motion,” Ph.D. Dissertation, Departmemt of Physiology, Albert Einstein College of Medicine, University Microfilms (1972).
3.Hirt, C.W., and Nichols, B.D. “Volume of fluid (VOF) method for dynamics of free boundaries,” Journal of Computational Physics, Vol. 39, pp. 201-225 (1981).
4.Ravoux, J.F., Nadim, A., and Haj-Hariri, H., “An Embedding Method for Bluff Body Flows: Interactions of Two Side-by-Side Cylinder Wakes,” Theoretical and Computational Fluid Dynamics, Vol. 16, pp. 433–466 (2003).
5.Choi, J.I., Oberoi, R.C., Edwards, J.R., and Rosati, J.A., “An immersed boundary method for complex incompressible flows,” Journal of Computational Physics, Vol. 224, pp. 757-784 (2007).
6.Viecelli, J.A., “A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique,” Journal of Computational Physics, Vol. 4, pp. 543-551 (1969).
7.Ye, T., Mittal, R., Udaykumar, H.S., and Shyy, W., “An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries,” Journal of Computational Physics, Vol. 156, pp. 209-240 (1999).
8.Peng, Y.F., Shiau, Y.H., and Hwang, R.R., “Transition in a 2-D lid-driven cavity flow,” Computers & Fluids, Vol. 32, pp. 337-352 (2003).
9.Ghia, U., Ghia, K.N., and Shin, C.T., “High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method,” Journal of Computational Physics, Vol. 48, pp. 387-411 (1982).
10.Wannier, G.H., “A contribution to the hydrodynamics of lubrication,” Quarterly of Applied Mathematics, Vol. 8, No. 1,pp.10-15 (1950).
11.Chen, J. H., Pritchard, W. G., and Tavener, S. J., “Bifurcation for flow past a cylinder between parallel planes,” Journal of Fluid Mechanics, Vol. 284, pp. 23-52 (1995).
12.Sakamoto, H., and Haniu, H., “Optimum suppression of fluid forces acting on a circular cylinder,” Journal of Fluids Enggineering, Vol. 116, pp. 221-227 (1994).
13.Young, D.L., Huang, J.L., and Eldho, T.I., “Simulation of laminar vortex shedding flow past cylinders using a coupled BEM and FEM model,” Computer Methods in Applied Mechanics and Engineering, Vol. 190, pp. 5975-5998 (2001).
14.Strykowski, B. J., and Sreenivasan, K. R., “On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers,” Journal of Fluid Mechanics, Vol. 218, pp. 71-107 (1990).
15.Sakamoto, H., Tan, K., and Haniu, H., “An optimum suppression of fluid forces by controlling a shear layer separated from a square prism,” Journal of Fluids Engineering, Vol. 113, pp. 183-9 (1991).
16.Sakamoto, H., and Haniu, H., “Optimum suppression of fluid forces acting on a circular cylinder,” Journal of Fluids Engineering, Vol. 116, pp. 221-7 (1994).
17.Dalton, C., Xu, Y., and Owen, J. C., “The Suppression of lift on a circular cylinder due to vortex shedding at moderate Reynolds numbers,” Journal of Fluids Structures, Vol. 15, pp. 61-28 (2001).
18.Zhao, M., Cheng, L., Teng, B., and Liang, D., “Numerical simulation of viscous flow past two circular cylinders of different diameters,” Applied Ocean Research, Vol. 27, pp. 39-55 (2005).
19.Delaunay, Y., and Kaiktsis, L., “Control of circular cylinder wakes using base mass transpiration,” Physics and Fluids, Vol. 13, pp. 3285-302 (2001).
20.Young, D. L., Huang, J. L., and Eldho, T. I., “Simulation of laminar vortex shedding flow past cylinders using a coupled BEM and FEM model,” Computer Methods in Applied Mechanics Engineering, Vol. 190, pp. 5975-98 (2001).
21.Lei, C., Cheng, L., and Kavanagh, K., “A finite difference solution of the shear flow over a circular cylinder,” Ocean Engineering, Vol. 27, pp. 271-90 (2000).